Risk and ReturnProblem Set 6 ECN 134Financial Economics Prof. Farshid MojaverOn Financial Crisis1- What was the role of deregulation in the financial crisis of 2008? 2- What is systemic risk? How did it happen during the financial crisis of 2008?3- Why housing prices increased so dramatically from 2001 to 2004? Risk and Return1. You consider investing in one of three portfolios X, Y, or Z, for one year. The following matrix givesthe means and standard deviations of annual returns in % for the three portfolios; annual returns aredistributed normally:X Y ZMean 5 7 5Std. Dev. 20 20 10Rank the three portfolios in order of the probability ofi) the one-year return being negative,ii) the one-year return being less than 5 %,iii) the one-year return being less than 10 %.(Hint) you do not need a table for the normal distribution to arrive at the correct answers to i) through iii)iv) Could you imagine a rational investor preferring X to Y?v) Could you imagine a rational investor preferring X to Z? vi) Could you imagine a risk-averse investor preferring X to Z?2. Based on the scenarios below, what is the expected return for a portfolio with the following returnprofile? Market ConditionBear Normal BullProbability 0.2 0.3 0.5Rate of return -25% 10% 24%Use the following scenario analysis for Stocks X and Y to answer Problems 3 through 5 (round tothe nearest percent)Bear MarketNormalMarketBull MarketProbability 0.2 0.5 0.3Stock X -20% 18% 50%Stock Y -15% 20% 10%3. What are the expected rates of return for Stocks X and Y?4. What are the standard deviations of returns on Stocks X and Y?5. Assume that of your $10,000 portfolio, you invest $9,000 in Stock X and $1,000 in Stock Y. What isthe expected return on your portfolio?Part A: Optimal Risky Portfolio1. Stocks offer an expected rate of return of 18%, with a SD of 22%. Gold offers an expected return of10% with a SD of 30%.a. In light of the apparent inefficiency of gold with respect to both mean return and volatility, wouldanyone hold gold? If so, demonstrate graphically why one would do so.b. Given the data above reanswer (a) with the additional assumption that the correlation coefficientbetween gold and stock equals 1. Draw a graph illustrating why one would or would not hold gold inone’s portfolio. Could this set of assumptions for expected return, SD, and correlation representequilibrium for the security market?2. Suppose you have a project that has 70% chance of doubling your investment in a year and 30%chance of halving your investment in a year. What is the standard deviation of the rate of return on thisinvestment?3. Suppose that you have $1 million and the following two opportunities from which to construct aportfolio: (a) Risk-free asset earning 12% per year, (b) Risky asset with expected return 30% per year andstandard deviation of 40%.If you construct a portfolio with a standard deviation of 30%, what is the expected rate of return?4. Statistics fro three stocks A, B, and C, are shown in the following tables. Standard Deviations of ReturnsStock A B CStandard Deviation 40% 20% 40% Correlations of ReturnsStock A B CA 1.00 0.90 0.50B 1.00 0.10C 1.00Based only on the information provided in the tables, and given a choice between a portfolio made up ofequal amounts of stocks A and B or a portfolio made up of equal amounts of stocks B and C, state whichportfolio you would recommend. Justify your choice.5. Input the data from the table into a spreadsheet. Compute the serial correlation in decade returns foreach asset class and for inflation. Also find the correlation between the returns of various asset classes.What do he data indicate?1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990sSmall-company Stocks (%) -3.72 7.28 20.63 19.01 13.72 8.75 12.46 13.84Large-company Stocks (%) 18.36 -1.25 9.11 19.41 7.84 5.90 17.60 18.20Long-term Government (%) 3.98 4.60 3.59 0.25 1.14 6.63 11.50 8.60Intermediate-term Govt (%) 3.77 3.91 1.70 1.11 3.41 6.11 12.01 7.74Treasury bills (%) 3.56 0.30 0.37 1.87 3.89 6.29 9.00 5.02Inflation (%) -1.00 -2.04 5.36 2.22 2.52 7.36 5.10 2.936. An investor’s portfolio consists of two assets, one (MSFT) producing computer software, and the other (GOOG) selling internet advertising. Ten years of hypothetical data on returns (in percent) for these two stocks are given below; save these data for use next week also.Date MSFT GOOG Date MSFT GOOG1998 4.64 5.98 2003 10.80 14.561999 10.80 12.74 2004 6.88 11.572000 8.88 9.10 2005 13.76 4.032001 10.32 9.88 2006 13.76 16.512002 9.36 6.11 2007 7.44 11.18a) Based on these data, what is the expected return on MSFT? GOOG?b) What is the variance of return for MSFT? The standard deviation? Do the same calculation for GOOG. (Be sure to use one less than the number of observations as the denominator in the variance formula.)c) What is the covariance of MSFT returns with GOOG returns? What is the correlation of the two returns? Write out the formulas you use explicitly.7. Non-CAMP Portfolio Return and Risk, Two Assets:a) What is the return and risk of a portfolio with no MSFT stock and all GOOG stock? No GOOG stock and all MSFT stock? (Use S.D.- not the variance - to characterize risk.)b) Evaluate the return and risk for each of the weight combinations below: MSFT: 0 .2 .5 .6 .7 1GOOG: 1 .8 .5 .4 .3 0Carry four digits. Table your results, with the two columns of weights next to the column of portfolio expected returns next to the portfolio standard deviation (risk).c) Plot the expected returns and risk tabled above. (Use some graph paper, or measure and draw lines very carefully, or use a spreadsheet. Fill in the gaps between the weights I had you calculate with your best guess.)d) On both the table and the graph, identify both the feasible set and the efficient set. Do they differ? Why or why not? (Assume that no risk free asset is available.)e) What proportion of MSFT would you hold? Why? Do we know what another investor would hold? Why or why not?f) Is it possible for the feasible set to be backward bending when the correlation between the returns of assets i and j is positive, i.e., when >0, or is it necessary for to be zero or negative? Use the numbers in the example you have just done in the parts above to show how your answer applies in this case.Part C: CAPM1. What must be the beta of a portfolio with E(rp)=18%, if rf=6% and E(rM)=14%?2. Are the following true or false? Explain.a. Stocks with a beta of zero offer an expected rate of return